CN103471723A - Novel method for forecasting daytime temperature and night temperature of stratosphere balloon - Google Patents

Abstract

A novel method for forecasting the daytime temperature and the night temperature of a stratosphere balloon comprises the steps of 1 providing assumption conditions of the novel method for forecasting the daytime temperature and the night temperature of the stratosphere balloon; 2 according to the use environment of the stratosphere balloon and basic knowledge of the engineering thermodynamics, determining the energy exchanging mechanism of the stratosphere balloon and all energy exchanging items; 3 establishing heat analysis models of the energy exchanging items respectively to obtain specific parameterized expression forms of all the energy exchanging items; 4 according to the principle of energy balance, an energy balance equation of the stratosphere balloon in daytime and an energy balance equation of the stratosphere balloon at night are established respectively; 5 substituting all the energy exchanging items obtained in the step 3 into the energy balance equations in the step 4, and then a simple iteration method in a numerical solution method is used for obtaining the daytime temperature of the stratosphere balloon and the night temperature of the stratosphere balloon. According to the novel method forecasting the daytime temperature and the night temperature of the stratosphere balloon, only bag cloth material parameters, the suspension height and the suspension time are needed, and then the daytime temperature and the night temperature of the stratosphere balloon can be obtained.

Description

A kind of new method of predicting the day and night temperature of stratosphere balloon

Technical field

The invention provides a kind of new method of predicting the day and night temperature of stratosphere balloon, belong to the aeronautical technology field.

Background technology

Stratosphere balloon is a kind of low cost, high efficiency aircraft, can carry out for a long time reconnaissance mission, carry out goods input etc., has boundless application potential and prospect, and therefore, correlation technique becomes the focus of studying this year.The temperature of stratosphere balloon when suspending is one of very crucial input parameter for the designer, and especially most important to choosing of its capsule cloth material, therefore, how to obtain effective temperature is all the problem that the engineering staff need to solve all the time.Can directly measure its temperature by the stratosphere balloon flight test, but experimentation cost is higher, and the cycle of wasting time and energy is long, also is difficult to all situations are all measured by test; Numerical simulation method need to be set up complicated finite element model, calculation of complex, and counting yield is low; More existing analytic methods, the factor that model is considered is comprehensive not, and theory solves also more complicated.Therefore, the present invention proposes a kind of analytic method of predicting the day and night temperature of stratosphere balloon, the method is very simple and practical, the capsule cloth material parameter, hoverheight and the time that only need a small amount of stratosphere balloon, just can be easy to obtain the day and night temperature of stratosphere balloon, visible the present invention has Important Academic meaning and engineering using value.

Summary of the invention

The invention provides a kind of new method of predicting the day and night temperature of stratosphere balloon, it is easy that the method has calculating, the precision advantages of higher, and its technical scheme is as follows:

A kind of new method of predicting the day and night temperature of stratosphere balloon of the present invention, the method concrete steps are as follows:

The assumed condition of the new method of the day and night temperature of step 1, proposition prediction stratosphere balloon.

Assumed condition comprises:

(1), when the stratosphere balloon stand under load, the actual similar water-drop-shaped of shape, for simplified model, be reduced to by stratosphere balloon the circle that radius is R.The characteristic dimension L of stratosphere balloon can mean with diameter;

(2) the capsule cloth due to stratosphere balloon is very thin, in micron dimension, therefore, supposes that the temperature of capsule cloth thickness direction is identical, does not consider the heat transmission between capsule cloth internal layer and skin;

(3) do not consider the loss of the inner helium of stratosphere balloon, the weight of supposing stratosphere balloon is constant;

(4) due to earth radius R _efor 6371.23km, and the sun apart from the earth the distance be 1.5 * 10 ⁸km, therefore, suppose that when sunshine arrives earth overhead be directional light;

(5) suppose that the earth is the thermal equilibrium body;

(6) do not consider the variation of intensity of solar radiation with solar radiation angle and atmospheric extinction coefficient;

(7) do not consider the impact of carbon dioxide and ozone infrared radiation.

Step 2, according to the environment for use of stratosphere balloon and the ABC of Engineering Thermodynamics, determine the energy exchange mechanism of stratosphere balloon and each energy exchange item.

Stratosphere balloon mainly carries out energy exchange by radiation and convection current, comprising: the direct solar radiation item Q that the stratosphere balloon episphere absorbs ₁(t) sun scattered radiation item Q that, stratosphere balloon absorbs ₂(t) earth reflected radiation item Q that, the stratosphere balloon lower semisphere absorbs ₃(t) earth infrared radiation item Q that, the stratosphere balloon lower semisphere absorbs ₄(t), the external infrared radiation item Q of stratosphere balloon ₅(t) the internal reflection infrared radiation item Q that, stratosphere balloon absorbs ₆(t), the convection heat transfer item Q between stratosphere balloon and outside atmosphere ₇and the convection heat transfer item Q between stratosphere balloon and internal gas (t) ₈(t).

Step 3, each energy exchange item proposed for step 2 are set up respectively its thermal model, obtain the concrete concrete Parameter Expression form of each energy exchange item.

The area of the infinitesimal of stratosphere balloon can be expressed as

In formula, dA is the unit dimension on stratosphere balloon, the latitude that θ is spherical coordinate system or solar radiation angle or sunshine and imfinitesimal method between angle,

longitude for spherical coordinate system.

The direct solar radiation that infinitesimal on the stratosphere balloon episphere absorbs is

dQ ₁(t)=α ₁τI ₀cosθdA (2)

In formula, α ₁for the capsule cloth of the stratosphere balloon absorptivity to direct solar radiation, τ is the atmosphere coefficient of transparency, I ₀for solar constant.

The sun scattered radiation that infinitesimal on stratosphere balloon absorbs is

dQ ₂(t)=α ₁I ₁dA (3)

In formula, I ₁for sun diffuse radiation.

The earth reflected radiation that infinitesimal on the stratosphere balloon lower semisphere absorbs is

$d{Q}_3\left(t\right)={\mathrm{\α}}_1{\mathrm{\ρ}}_g\mathrm{\τ}{I}_0{\left(\frac{R_e}{R_e+H}\right)}^2\cos \mathrm{\θ}\cos \mathrm{\φdA}---\left(4\right)$

In formula, ρ _gfor ground surface reflectance mean value, R _efor earth radius, the hoverheight of H stratosphere balloon, φ is the angle between sunshine direction and ground ball center peace fluid layer balloon center line connecting direction.

The earth infrared radiation that infinitesimal on the stratosphere balloon lower semisphere absorbs is

$d{Q}_4\left(t\right)={\mathrm{\α}}_2\mathrm{\τ}{I}_0{R}_e^2\frac{1-{\mathrm{\ρ}}_g}{4{(R_e+H)}^2}\cos \mathrm{\θdA}---\left(5\right)$

In formula, α ₂for the capsule cloth of the stratosphere balloon absorptivity to infrared radiation.

The external infrared radiation of infinitesimal on stratosphere balloon is

$d{Q}_5\left(t\right)=2\mathrm{\ϵ\σ}{T}_1^4\mathrm{dA}---\left(6\right)$

In formula, the emissivity of the capsule cloth that ε is stratosphere balloon to infrared radiation, σ is Si Difen-Boltzmann constant, T ₁capsule Bu Wendu for stratosphere balloon.

The internal reflection infrared radiation that infinitesimal on stratosphere balloon absorbs is

$d{Q}_6\left(t\right)=\frac{{\mathrm{\α}}_2\mathrm{\ϵ\σ}{T}_1^4}{1-r}\mathrm{dA}---\left(7\right)$

In formula, the reflectivity that r is stratosphere balloon.

Infinitesimal and the convection heat transfer between outside atmosphere on stratosphere balloon are

dQ ₇(t)=h ₁(T ₁-T ₂)dA (8)

In formula, h ₁for the convection transfer rate between stratosphere balloon and outside atmosphere, T ₂temperature for outside atmosphere.

Convection heat transfer between infinitesimal on stratosphere balloon and inner helium is

dQ ₈(t)=h ₂(T ₁-T ₃)dA (9)

In formula, h ₂for the convection transfer rate between stratosphere balloon and inner helium, T ₃temperature for inner helium.

Sun diffuse radiation I in formula (3) ₁can be expressed as

$I_1=\frac{1}{2}{I}_0\cos \mathrm{\θ}{\cos }^2\frac{\mathrm{\θ}}{2}---\left(10\right)$

Included angle between sunshine direction in formula (4) and ground ball center peace fluid layer balloon center line connecting direction can be expressed as

$\mathrm{\φ}=\frac{\mathrm{\π}|12-t|}{12},(6a.m.\≤t\≤18p.m.)---\left(11\right)$

In formula, t means the time, and from the 6:00 AM to the afternoon, 18 is the cycle on a daytime.

H in formula (8) and formula (9) ₁and h ₂can be expressed as respectively

$h_1=N{u}_1\frac{{\mathrm{\λ}}_1}{L}---\left(12\right)$

$h_2=N{u}_1\frac{{\mathrm{\λ}}_1}{L}---\left(13\right)$

In formula, Nu ₁for the Nusselt number of forced convection, λ ₁for the heat-conduction coefficient of forced convection, Nu ₂for the Nusselt number of free convection, λ ₂heat-conduction coefficient for free convection.

In the heat of stratosphere balloon is analyzed, solar constant I ₀for 1367W/m ², atmosphere coefficient of transparency τ is 0.9, ground surface reflectance mean value ρ _gbe that 0.3, Si Difen-Boltzmann constant σ is 5.6696 * 10 ^-8w(m ²k ⁴), the capsule cloth of stratosphere balloon equates with absorptivity the emissivity of infrared radiation, i.e. ε=α ₂.

Respectively formula (2) to formula (9) is carried out to integration, and the substitution correlation parameter, can obtain the total amount of each energy exchange item:

$Q_1\left(t\right)=\left\{\begin{array}{c}1230.3\mathrm{\π}{R}^2{\mathrm{\α}}_1,(6a.m.\≤t\≤18p.m.)\\ 0\end{array}\right.---\left(13\right)$

$Q_2\left(t\right)=\left\{\begin{array}{c}1139.2\mathrm{\π}{\mathrm{\α}}_1{R}^2,(6a.m.\≤t\≤18p.m.)\\ 0\end{array}\right.---\left(14\right)$

$Q_3\left(t\right)=\left\{\begin{array}{c}366.8\mathrm{\π}{R^2\mathrm{\α}}_1{\left(\frac{R_e}{R_e+H}\right)}^2\cos \frac{\mathrm{\π}|12-t|}{12},(6a.m.\≤t\≤18p.m.)\\ 0\end{array}\right.---\left(15\right)$

$Q_5\left(t\right)=\underset{A}{\∫}2\mathrm{\ϵ\σ}{T}_1^4\mathrm{dA}=2\mathrm{A\ϵA\σ}{T}_1^4=45.4\mathrm{\π}{R}^2{\mathrm{\α}}_2\×{10}^{-8}{T}_1^4---\left(17\right)$

$Q_6\left(t\right)=\underset{A}{\∫}\frac{{\mathrm{\α}}_2\mathrm{\ϵ\σ}{T}_1^4}{1-r}\mathrm{dA}=\frac{A{\mathrm{\α}}_2\mathrm{\ϵ\σ}{T}_1^4}{1-r}=\frac{22.7\mathrm{\π}{R}^2{\mathrm{\α}}_2\mathrm{\ϵ}\×{10}^{-8}{T}_1^4}{1-r}---\left(19\right)$

$Q_7\left(t\right)=\underset{A}{\∫}{h}_1(T_1-T_2)\mathrm{dA}=A{h}_1(T_1-T_2)=4\mathrm{\π}{R}^2{h}_1(T_1-T_2)---\left(20\right)$

$Q_8\left(t\right)=\underset{A}{\∫}{h}_2(T_1-T_3)\mathrm{dA}=A{h}_2(T_1-T_3)=4\mathrm{\π}{R}^2{h}_2(T_1-T_3)---\left(21\right)$

Wherein, the infinitesimal described in step 3 refers to the small unit intercepted on stratosphere balloon, and area is infinitely small.

Step 4, according to principle of energy balance, set up respectively stratosphere balloon by day with the energy-balance equation at night.

For daytime, the gross energy of the capsule cloth of stratosphere balloon is

△Q _film(t)=Q ₁(t)+Q ₂(t)+Q ₃(t)+Q ₄(t)-Q ₅(t)+Q ₆(t)-Q ₇(t)-Q ₈(t) (22)

The gross energy of the inside helium of stratosphere balloon is

△Q _gas(t)=Q ₈(t) (23)

When the energy exchange of stratosphere balloon reaches equilibrium state, △ Q _film(t)=0, △ Q _gas(t)=0, substitution formula (22) and formula (23) can obtain capsule cloth and inner helium energy-balance equation by day about stratosphere balloon:

$\left\{\begin{array}{c}{Q}_1\left(t\right)+Q_2\left(t\right)+Q_3\left(t\right)+Q_4\left(t\right)-Q_5\left(t\right)+Q_6\left(t\right)-Q_7\left(t\right)-Q_8\left(t\right)=0\\ Q_8\left(t\right)=0\end{array}\right.---\left(24\right)$

For night, there is no direct solar radiation, sun scattered radiation and earth reflected radiation, i.e. Q ₁(t)=0, Q ₂(t)=0, Q ₃(t)=0, therefore, the capsule cloth of stratosphere balloon and inner helium at the energy-balance equation at night are

$\left\{\begin{array}{c}{Q}_4\left(t\right)-Q_5\left(t\right)+Q_6\left(t\right)-Q_7\left(t\right)-Q_8\left(t\right)=0\\ Q_8\left(t\right)=0\end{array}\right.---\left(25\right)$

Energy-balance equation (24), (25) of step 5, each energy exchange item substitution step 4 that step 3 is obtained, the simple process of iteration in the recycling method of value solving can try to achieve stratosphere balloon by day with the temperature at night.

Formula (13) to formula (21) is updated to respectively in formula (24) and formula (25), can obtains

$\left\{\begin{array}{c}(\frac{22.7\mathrm{\π}{R}^2{\mathrm{\α}}_2\mathrm{\ϵ}\×{10}^{-8}}{1-r}-45.4\mathrm{\π}{R}^2{\mathrm{\α}}_2\×{10}^{-8})T_1^4-4\mathrm{\π}{R}^2{h}_1{T}_1+[366.8\mathrm{\π}{R}^2{\mathrm{\α}}_1{\left(\frac{R_e}{R_e+H}\right)}^2\cos \frac{\mathrm{\π}|12-t|}{12}\\ +2369.5\mathrm{\π}{R}^2{\mathrm{\α}}_1+214.0\mathrm{\π}{R}^2{\mathrm{\α}}_2{\left(\frac{R_e}{R_e+H}\right)}^2+4\mathrm{\π}{R}^2{h}_1{T}_2]=0\\ T_1-T_3=0\end{array}\right.$

(26)

$\left\{\begin{array}{c}(\frac{22.7\mathrm{\π}{R}^2{\mathrm{\α}}_2\mathrm{\ϵ}\×{10}^{-8}}{1-r}-45.4\mathrm{\π}{R}^2{\mathrm{\α}}_2\×{10}^{-8})T_1^4-4\mathrm{\π}{R}^2{h}_1{T}_1+[214.0\mathrm{\π}{R}^2{\mathrm{\α}}_2{\left(\frac{R_e}{R_e+H}\right)}^2+4\mathrm{\π}{R}^2{h}_1{T}_2]=0\\ T_1-T_3=0\end{array}\right.$

(27)

From (26) and formula (27), when the energy exchange of stratosphere balloon reaches equilibrium state, the capsule Bu Wendu of the stratosphere balloon of day and night equates with inner helium temperature.By the simple process of iteration in method of value solving, equation (26) and (27) are solved respectively, can obtain stratosphere balloon by day with capsule Bu Wendu and the inner helium temperature at night.

A kind of new method of predicting the day and night temperature of stratosphere balloon of the present invention, be characterized in very simple and practical, the capsule cloth material parameter, hoverheight and the time that only need a small amount of stratosphere balloon, just can be easy to obtain the day and night temperature of stratosphere balloon.

The accompanying drawing explanation

True form schematic diagram when Fig. 1 a is the stratosphere balloon stand under load.

Simplification shape schematic diagram when Fig. 1 b is the stratosphere balloon stand under load.

Fig. 2 is stratosphere balloon energy exchange schematic diagram.

Fig. 3 is the stratosphere balloon surface infinitesimal schematic diagram that is subject to solar light irradiation

The solar radiation angle schematic diagram that Fig. 4 is stratosphere balloon surface infinitesimal.

Fig. 5 is the relative position schematic diagram between stratosphere balloon and the earth and the sun.

Fig. 6 is to be the FB(flow block) of the method for the invention.

In figure, symbol description is as follows:

R in Fig. 1 b is the stratosphere balloon radius.

Q in Fig. 2 ₁(t) the direct solar radiation item absorbed for the stratosphere balloon episphere, Q ₂(t) sun scattered radiation item absorbed for stratosphere balloon, Q ₃(t) earth reflected radiation item absorbed for the stratosphere balloon lower semisphere, Q ₄(t) earth infrared radiation item absorbed for the stratosphere balloon lower semisphere, Q ₅(t) be the external infrared radiation item of stratosphere balloon, Q ₆(t) the internal reflection infrared radiation item absorbed for stratosphere balloon, Q ₇(t) be the convection heat transfer item between stratosphere balloon and outside atmosphere, Q ₈(t) be the convection heat transfer item between stratosphere balloon and internal gas.

DA in Fig. 3 is the unit dimension on stratosphere balloon, the normal direction that n is the infinitesimal on stratosphere balloon, the latitude that θ is spherical coordinate system or solar radiation angle or sunshine and imfinitesimal method between angle,

longitude for spherical coordinate system.

θ in Fig. 4 for for the latitude of spherical coordinate system or solar radiation angle or sunshine and imfinitesimal method between angle;

φ in Fig. 5 is the angle between sunshine direction and ground ball center peace fluid layer balloon center line connecting direction.

Embodiment

The FB(flow block) that Fig. 6 is the method for the invention, the present invention divides five steps to realize, is specially:

The assumed condition of the new method of the day and night temperature of step 1, proposition prediction stratosphere balloon.

Assumed condition comprises:

(1), during the stratosphere balloon stand under load, the actual similar water-drop-shaped of shape (as shown in Figure 1a), for simplified model, be reduced to by stratosphere balloon the circle (as shown in Figure 1 b) that radius is R.The characteristic dimension L of stratosphere balloon can mean with diameter;

(2) the capsule cloth due to stratosphere balloon is very thin, in micron dimension, therefore, supposes that the temperature of capsule cloth thickness direction is identical, does not consider the heat transmission between capsule cloth internal layer and skin;

(3) do not consider the loss of the inner helium of stratosphere balloon, the weight of supposing stratosphere balloon is constant;

(4) due to earth radius R _efor 6371.23km, and the sun apart from the earth the distance be 1.5 * 10 ⁸km, therefore, suppose that when sunshine arrives earth overhead be directional light;

(5) suppose that the earth is the thermal equilibrium body;

(6) do not consider the variation of intensity of solar radiation with solar radiation angle and atmospheric extinction coefficient;

(7) do not consider the impact of carbon dioxide and ozone infrared radiation.

Step 2, according to the environment for use of stratosphere balloon and the ABC of Engineering Thermodynamics, be defined as the energy exchange mechanism of stratosphere balloon and each energy exchange item.

Stratosphere balloon mainly carries out energy exchange by radiation and convection current, comprising: the direct solar radiation item Q that the stratosphere balloon episphere absorbs ₁(t) sun scattered radiation item Q that, stratosphere balloon absorbs ₂(t) earth reflected radiation item Q that, the stratosphere balloon lower semisphere absorbs ₃(t) earth infrared radiation item Q that, the stratosphere balloon lower semisphere absorbs ₄(t), the external infrared radiation item Q of stratosphere balloon ₅(t) the internal reflection infrared radiation item Q that, stratosphere balloon absorbs ₆(t), the convection heat transfer item Q between stratosphere balloon and outside atmosphere ₇and the convection heat transfer item Q between stratosphere balloon and internal gas (t) ₈(t).Provided stratosphere balloon energy exchange schematic diagram in Fig. 2.

Step 3, each energy exchange item proposed for step 1 are set up respectively its thermal model, obtain the concrete concrete Parameter Expression form of each energy exchange item.

In Fig. 2 and Fig. 3, provided the infinitesimal of stratosphere balloon, its area can be expressed as

in formula, dA is the unit dimension on stratosphere balloon, the latitude that θ is spherical coordinate system or solar radiation angle or sunshine and imfinitesimal method between angle,

longitude for spherical coordinate system.

The direct solar radiation that infinitesimal on the stratosphere balloon episphere absorbs is

DQ ₁(t)=α ₁τ I ₀in cos θ dA (2) formula, α ₁for the capsule cloth of the stratosphere balloon absorptivity to direct solar radiation, τ is the atmosphere coefficient of transparency, I ₀for solar constant.

The sun scattered radiation that infinitesimal on stratosphere balloon absorbs is

DQ ₂(t)=α ₁i ₁in dA (3) formula, I ₁for sun diffuse radiation.

The earth reflected radiation that infinitesimal on the stratosphere balloon lower semisphere absorbs is

$d{Q}_3\left(t\right)={\mathrm{\α}}_1{\mathrm{\ρ}}_g\mathrm{\τ}{I}_0{\left(\frac{R_e}{R_e+H}\right)}^2\cos \mathrm{\θ}\cos \mathrm{\φdA}---\left(4\right)$

In formula, ρ _gfor ground surface reflectance mean value, R _efor earth radius, the hoverheight of H stratosphere balloon, φ is the angle between sunshine direction and ground ball center peace fluid layer balloon center line connecting direction, the position relationship between the earth, stratosphere balloon and sun three is as shown in Figure 5.The solar radiation angle schematic diagram that Fig. 4 is stratosphere balloon surface infinitesimal.

The earth infrared radiation that infinitesimal on the stratosphere balloon lower semisphere absorbs is

$d{Q}_4\left(t\right)={\mathrm{\α}}_2\mathrm{\τ}{I}_0{R}_e^2\frac{1-{\mathrm{\ρ}}_g}{4{(R_e+H)}^2}\cos \mathrm{\θdA}---\left(5\right)$

In formula, α ₂for the capsule cloth of the stratosphere balloon absorptivity to infrared radiation.

The external infrared radiation of infinitesimal on stratosphere balloon is

$d{Q}_5\left(t\right)=2\mathrm{\ϵ\σ}{T}_1^4\mathrm{dA}---\left(6\right)$

In formula, the emissivity of the capsule cloth that ε is stratosphere balloon to infrared radiation, σ is Si Difen-Boltzmann constant, T ₁capsule Bu Wendu for stratosphere balloon.

The internal reflection infrared radiation that infinitesimal on stratosphere balloon absorbs is

$d{Q}_6\left(t\right)=\frac{{\mathrm{\α}}_2\mathrm{\ϵ\σ}{T}_1^4}{1-r}\mathrm{dA}---\left(7\right)$

In formula, the reflectivity that r is stratosphere balloon.

Infinitesimal and the convection heat transfer between outside atmosphere on stratosphere balloon are

dQ ₇(t)=h ₁(T ₁-T ₂)dA (8)

In formula, h ₁for the convection transfer rate between stratosphere balloon and outside atmosphere, T ₂temperature for outside atmosphere.

Convection heat transfer between infinitesimal on stratosphere balloon and inner helium is

dQ ₈(t)=h ₂(T ₁-T ₃)dA (9)

In formula, h ₂for the convection transfer rate between stratosphere balloon and inner helium, T ₃temperature for inner helium.

Sun diffuse radiation I in formula (3) ₁can be expressed as

$I_1=\frac{1}{2}{I}_0\cos \mathrm{\θ}{\cos }^2\frac{\mathrm{\θ}}{2}---\left(10\right)$

Included angle between sunshine direction in formula (4) and ground ball center peace fluid layer balloon center line connecting direction can be expressed as

$\mathrm{\φ}=\frac{\mathrm{\π}|12-t|}{12},(6a.m.\≤t\≤18p.m.)---\left(11\right)$

In formula, t means the time, and from the 6:00 AM to the afternoon, 18 is the cycle on a daytime.

H in formula (8) and formula (9) ₁and h ₂can be expressed as respectively

$h_1=N{u}_1\frac{{\mathrm{\λ}}_1}{L}---\left(12\right)$

$h_2=N{u}_1\frac{{\mathrm{\λ}}_1}{L}---\left(13\right)$

In formula, Nu ₁for the Nusselt number of forced convection, λ ₁for the heat-conduction coefficient of forced convection, Nu ₂for the Nusselt number of free convection, λ ₂heat-conduction coefficient for free convection.

The heat-conduction coefficient of forced convection can be expressed as

${\mathrm{\λ}}_1=0.0241{\left(\frac{T_2}{273.15}\right)}^{0.9}---\left(14\right)$

The Nusselt number of forced convection can be expressed as

Nu ₁=(0.037Re ^4/5-817.0)Pr ^1/3 (15)

In formula, Re is Reynolds number, the Prandtl number that Pr is atmosphere.

The Prandtl number of atmosphere can be expressed as

Pr=0.804-3.25×10 ^-4T ₂ (16)

Reynolds number can be expressed as

$\mathrm{Re}=\frac{\mathrm{VL}}{v}---\left(17\right)$

In formula, the flowing velocity that V is the stratosphere balloon ambient atmosphere, the characteristic dimension that L is stratosphere balloon, the kinetic viscosity that ν is the stratosphere atmosphere.

The kinetic viscosity of stratosphere atmosphere can be expressed as

$v=\frac{1.46\×{10}^{-6}{T}_2^{1.5}}{{\mathrm{\ρ}}_1(T_2+110.4)}---\left(18\right)$

In formula, ρ ₁density for atmosphere.

The temperature of normal atmosphere and density T ₂and ρ ₁with the stratosphere balloon hoverheight, H can be expressed as respectively

$\left\{\begin{array}{cc}{T}_2=288.15-6.5H& H\∈\left[\mathrm{0,11}\mathrm{km}\right)\\ T_2=216.65& H\∈[11\mathrm{km},20\mathrm{km})\\ T_2=216.65+(H-20)& H\∈[20\mathrm{km},32\mathrm{km})\end{array}\right.---\left(19\right)$

$\left\{\begin{array}{cc}{\mathrm{\ρ}}_1=1.225\×{\left(\frac{288.15-6.5H}{288.15}\right)}^{4.25588}& H\∈\left[\mathrm{0,11}\mathrm{km}\right)\\ {\mathrm{\ρ}}_1=0.364\×e^{-\frac{H-11}{6.34162}}& H\∈[11\mathrm{km},20\mathrm{km})\\ {\mathrm{\ρ}}_1=0.088\×{\left[\frac{216.65+(H-20)}{216.65}\right]}^{-35.1632}& H\∈[20\mathrm{km},32\mathrm{km})\end{array}\right.---\left(20\right)$

While due to stratosphere balloon, reaching energy equilibrium, the free convection energy exchange of its inner helium and capsule cloth is 0, so do not need to provide the expression of the heat-conduction coefficient of the Nusselt number of free convection and free convection again.

In the heat of stratosphere balloon is analyzed, solar constant I ₀for 1367W/m ², atmosphere coefficient of transparency τ is 0.9, ground surface reflectance mean value ρ _gbe that 0.3, Si Difen-Boltzmann constant σ is 5.6696 * 10 ^-8w(m ²k ⁴), the capsule cloth of stratosphere balloon equates with absorptivity the emissivity of infrared radiation, i.e. ε=α ₂.

Respectively formula (2) to formula (9) is carried out to integration, and the substitution correlation parameter, can obtain the total amount of each energy exchange item:

$Q_1\left(t\right)=\left\{\begin{array}{c}1230.3\mathrm{\π}{R}^2{\mathrm{\α}}_1,(6a.m.\≤t\≤18p.m.)\\ 0\end{array}\right.---\left(21\right)$

$Q_2\left(t\right)=\left\{\begin{array}{c}1139.2\mathrm{\π}{\mathrm{\α}}_1{R}^2,(6a.m.\≤t\≤18p.m.)\\ 0\end{array}\right.---\left(22\right)$

$Q_3\left(t\right)=\left\{\begin{array}{c}366.8\mathrm{\π}{R^2\mathrm{\α}}_1{\left(\frac{R_e}{R_e+H}\right)}^2\cos \frac{\mathrm{\π}|12-t|}{12},(6a.m.\≤t\≤18p.m.)\\ 0\end{array}\right.---\left(23\right)$

$Q_5\left(t\right)=\underset{A}{\∫}2\mathrm{\ϵ\σ}{T}_1^4\mathrm{dA}=2\mathrm{A\ϵA\σ}{T}_1^4=45.4\mathrm{\π}{R}^2{\mathrm{\α}}_2\×{10}^{-8}{T}_1^4---\left(25\right)$

$Q_6\left(t\right)=\underset{A}{\∫}\frac{{\mathrm{\α}}_2\mathrm{\ϵ\σ}{T}_1^4}{1-r}\mathrm{dA}=\frac{A{\mathrm{\α}}_2\mathrm{\ϵ\σ}{T}_1^4}{1-r}=\frac{22.7\mathrm{\π}{R}^2{\mathrm{\α}}_2\mathrm{\ϵ}\×{10}^{-8}{T}_1^4}{1-r}---\left(26\right)$

$Q_7\left(t\right)=\underset{A}{\∫}{h}_1(T_1-T_2)\mathrm{dA}=A{h}_1(T_1-T_2)=4\mathrm{\π}{R}^2{h}_1(T_1-T_2)---\left(27\right)$

$Q_8\left(t\right)=\underset{A}{\∫}{h}_2(T_1-T_3)\mathrm{dA}=A{h}_2(T_1-T_3)=4\mathrm{\π}{R}^2{h}_2(T_1-T_3)---\left(28\right)$

Wherein, the infinitesimal described in step 3 refers to the small unit intercepted on stratosphere balloon, and area is infinitely small.

Step 4, according to principle of energy balance, set up respectively stratosphere balloon by day with the energy-balance equation at night.

For daytime, the gross energy of the capsule cloth of stratosphere balloon is

△Q _film(t)=Q ₁(t)+Q ₂(t)+Q ₃(t)+Q ₄(t)-Q ₅(t)+Q ₆(t)-Q ₇(t)-Q ₈(t) (29)

The gross energy of the inside helium of stratosphere balloon is

△Q _gas(t)=Q ₈(t) (30)

When the energy exchange of stratosphere balloon reaches equilibrium state, △ Q _film(t)=0, △ Q _gas(t)=0, substitution formula (29) and formula (30) can obtain capsule cloth and inner helium energy-balance equation by day about stratosphere balloon:

$\left\{\begin{array}{c}{Q}_1\left(t\right)+Q_2\left(t\right)+Q_3\left(t\right)+Q_4\left(t\right)-Q_5\left(t\right)+Q_6\left(t\right)-Q_7\left(t\right)-Q_8\left(t\right)=0\\ Q_8\left(t\right)=0\end{array}\right.---\left(31\right)$

For night, there is no direct solar radiation, sun scattered radiation and earth reflected radiation, i.e. Q ₁(t)=0, Q ₂(t)=0, Q ₃(t)=0, therefore, the capsule cloth of stratosphere balloon and inner helium at the energy-balance equation at night are

$\left\{\begin{array}{c}{Q}_4\left(t\right)-Q_5\left(t\right)+Q_6\left(t\right)-Q_7\left(t\right)-Q_8\left(t\right)=0\\ Q_8\left(t\right)=0\end{array}\right.---\left(32\right)$

The energy-balance equation of step 5, each energy exchange item substitution step 4 that step 3 is obtained, the simple process of iteration in the recycling method of value solving can try to achieve stratosphere balloon by day with the temperature at night.

Formula (21) to formula (28) is updated to respectively in formula (31) and formula (32), can obtains

$\left\{\begin{array}{c}(\frac{22.7\mathrm{\π}{R}^2{\mathrm{\α}}_2\mathrm{\ϵ}\×{10}^{-8}}{1-r}-45.4\mathrm{\π}{R}^2{\mathrm{\α}}_2\×{10}^{-8})T_1^4-4\mathrm{\π}{R}^2{h}_1{T}_1+[366.8\mathrm{\π}{R}^2{\mathrm{\α}}_1{\left(\frac{R_e}{R_e+H}\right)}^2\cos \frac{\mathrm{\π}|12-t|}{12}\\ +2369.5\mathrm{\π}{R}^2{\mathrm{\α}}_1+214.0\mathrm{\π}{R}^2{\mathrm{\α}}_2{\left(\frac{R_e}{R_e+H}\right)}^2+4\mathrm{\π}{R}^2{h}_1{T}_2]=0\\ T_1-T_3=0\end{array}\right.$

(33)

$\left\{\begin{array}{c}(\frac{22.7\mathrm{\π}{R}^2{\mathrm{\α}}_2\mathrm{\ϵ}\×{10}^{-8}}{1-r}-45.4\mathrm{\π}{R}^2{\mathrm{\α}}_2\×{10}^{-8})T_1^4-4\mathrm{\π}{R}^2{h}_1{T}_1+[214.0\mathrm{\π}{R}^2{\mathrm{\α}}_2{\left(\frac{R_e}{R_e+H}\right)}^2+4\mathrm{\π}{R}^2{h}_1{T}_2]=0\\ T_1-T_3=0\end{array}\right.$

(34)

From (33) and formula (34), when the energy exchange of stratosphere balloon reaches equilibrium state, the capsule Bu Wendu of the stratosphere balloon of day and night equates with inner helium temperature.By the simple process of iteration in method of value solving, equation (33) and (34) are solved respectively, can obtain stratosphere balloon by day with capsule Bu Wendu and the inner helium temperature at night.

Claims (1)

1. a new method of predicting the day and night temperature of stratosphere balloon, it is characterized in that: the method concrete steps are as follows:

The assumed condition of the new method of the day and night temperature of step 1, proposition prediction stratosphere balloon;

Assumed condition comprises:

(1) when the stratosphere balloon stand under load, the actual similar water-drop-shaped of shape, for simplified model, be reduced to by stratosphere balloon the circle that radius is R, and the characteristic dimension L of stratosphere balloon means with diameter;

(2) the capsule cloth due to stratosphere balloon is very thin, and in micron dimension, therefore, the temperature of establishing capsule cloth thickness direction is identical, does not consider the heat transmission between capsule cloth internal layer and skin;

(3) do not consider the loss of the inner helium of stratosphere balloon, the weight of establishing stratosphere balloon is constant;

(4) due to earth radius R _efor 6371.23km, and the sun apart from the earth the distance be 1.5 * 10 ⁸therefore km, is directional light while establishing sunshine arrival earth overhead;

(5) establishing the earth is the thermal equilibrium body;

(6) do not consider the variation of intensity of solar radiation with solar radiation angle and atmospheric extinction coefficient;

(7) do not consider the impact of carbon dioxide and ozone infrared radiation;

Step 2, according to the environment for use of stratosphere balloon and the ABC of Engineering Thermodynamics, determine the energy exchange mechanism of stratosphere balloon and each energy exchange item;

Stratosphere balloon carries out energy exchange by radiation and convection current, comprising: the direct solar radiation item Q that the stratosphere balloon episphere absorbs ₁(t) sun scattered radiation item Q that, stratosphere balloon absorbs ₂(t) earth reflected radiation item Q that, the stratosphere balloon lower semisphere absorbs ₃(t) earth infrared radiation item Q that, the stratosphere balloon lower semisphere absorbs ₄(t), the external infrared radiation item Q of stratosphere balloon ₅(t) the internal reflection infrared radiation item Q that, stratosphere balloon absorbs ₆(t), the convection heat transfer item Q between stratosphere balloon and outside atmosphere ₇and the convection heat transfer item Q between stratosphere balloon and internal gas (t) ₈(t);

Step 3, each energy exchange item proposed for step 2 are set up respectively its thermal model, obtain the concrete concrete Parameter Expression form of each energy exchange item;

The cartographic represenation of area of the infinitesimal of stratosphere balloon is

In formula, dA is the unit dimension on stratosphere balloon, the latitude that θ is spherical coordinate system or solar radiation angle or sunshine and imfinitesimal method between angle,

longitude for spherical coordinate system;

The direct solar radiation that infinitesimal on the stratosphere balloon episphere absorbs is

dQ ₁(t)=α ₁τI ₀cosθdA (2)

In formula, α ₁for the capsule cloth of the stratosphere balloon absorptivity to direct solar radiation, τ is the atmosphere coefficient of transparency, I ₀for solar constant;

The sun scattered radiation that infinitesimal on stratosphere balloon absorbs is

dQ ₂(t)=α ₁I ₁dA (3)

In formula, I ₁for sun diffuse radiation;

The earth reflected radiation that infinitesimal on the stratosphere balloon lower semisphere absorbs is

$d{Q}_3\left(t\right)={\mathrm{\α}}_1{\mathrm{\ρ}}_g\mathrm{\τ}{I}_0{\left(\frac{R_e}{R_e+H}\right)}^2\cos \mathrm{\θ}\cos \mathrm{\φdA}---\left(4\right)$

In formula, ρ _gfor ground surface reflectance mean value, R _efor earth radius, the hoverheight of H stratosphere balloon, φ is the angle between sunshine direction and ground ball center peace fluid layer balloon center line connecting direction;

The earth infrared radiation that infinitesimal on the stratosphere balloon lower semisphere absorbs is

$d{Q}_4\left(t\right)={\mathrm{\α}}_2\mathrm{\τ}{I}_0{R}_e^2\frac{1-{\mathrm{\ρ}}_g}{4{(R_e+H)}^2}\cos \mathrm{\θdA}---\left(5\right)$

In formula, α ₂for the capsule cloth of the stratosphere balloon absorptivity to infrared radiation;

The external infrared radiation of infinitesimal on stratosphere balloon is

$d{Q}_5\left(t\right)=2\mathrm{\ϵ\σ}{T}_1^4\mathrm{dA}---\left(6\right)$

In formula, the emissivity of the capsule cloth that ε is stratosphere balloon to infrared radiation, σ is Si Difen-Boltzmann constant, T ₁capsule Bu Wendu for stratosphere balloon;

The internal reflection infrared radiation that infinitesimal on stratosphere balloon absorbs is

$d{Q}_6\left(t\right)=\frac{{\mathrm{\α}}_2\mathrm{\ϵ\σ}{T}_1^4}{1-r}\mathrm{dA}---\left(7\right)$

In formula, the reflectivity that r is stratosphere balloon;

Infinitesimal and the convection heat transfer between outside atmosphere on stratosphere balloon are

dQ ₇(t)=h ₁(T ₁-T ₂)dA (8)

In formula, h ₁for the convection transfer rate between stratosphere balloon and outside atmosphere, T ₂temperature for outside atmosphere;

Convection heat transfer between infinitesimal on stratosphere balloon and inner helium is

dQ ₈(t)=h ₂(T ₁-T ₃)dA (9)

In formula, h ₂for the convection transfer rate between stratosphere balloon and inner helium, T ₃temperature for inner helium;

Sun diffuse radiation I in formula (3) ₁be expressed as

$I_1=\frac{1}{2}{I}_0\cos \mathrm{\θ}{\cos }^2\frac{\mathrm{\θ}}{2}---\left(10\right)$

Included angle between sunshine direction in formula (4) and ground ball center peace fluid layer balloon center line connecting direction is expressed as

$\mathrm{\φ}=\frac{\mathrm{\π}|12-t|}{12},(6a.m.\≤t\≤18p.m.)---\left(11\right)$

In formula, t means the time, and from the 6:00 AM to the afternoon, 18 is the cycle on a daytime;

H in formula (8) and formula (9) ₁and h ₂be expressed as respectively

$h_1=N{u}_1\frac{{\mathrm{\λ}}_1}{L}---\left(12\right)$

$h_2=N{u}_1\frac{{\mathrm{\λ}}_1}{L}---\left(13\right)$

In formula, Nu ₁for the Nusselt number of forced convection, λ ₁for the heat-conduction coefficient of forced convection, Nu ₂for the Nusselt number of free convection, λ ₂heat-conduction coefficient for free convection;

In the heat of stratosphere balloon is analyzed, solar constant I ₀for 1367W/m ², atmosphere coefficient of transparency τ is 0.9, ground surface reflectance mean value ρ _gbe that 0.3, Si Difen-Boltzmann constant σ is 5.6696 * 10 ^-8w(m ²k ⁴), the capsule cloth of stratosphere balloon equates with absorptivity the emissivity of infrared radiation, i.e. ε=α ₂;

Respectively formula (2) to formula (9) is carried out to integration, and the substitution correlation parameter, obtains the total amount of each energy exchange item:

$Q_1\left(t\right)=\left\{\begin{array}{c}1230.3\mathrm{\π}{R}^2{\mathrm{\α}}_1,(6a.m.\≤t\≤18p.m.)\\ 0\end{array}\right.---\left(13\right)$

$Q_2\left(t\right)=\left\{\begin{array}{c}1139.2\mathrm{\π}{\mathrm{\α}}_1{R}^2,(6a.m.\≤t\≤18p.m.)\\ 0\end{array}\right.---\left(14\right)$

$Q_3\left(t\right)=\left\{\begin{array}{c}366.8\mathrm{\π}{R^2\mathrm{\α}}_1{\left(\frac{R_e}{R_e+H}\right)}^2\cos \frac{\mathrm{\π}|12-t|}{12},(6a.m.\≤t\≤18p.m.)\\ 0\end{array}\right.---\left(15\right)$

$Q_5\left(t\right)=\underset{A}{\∫}2\mathrm{\ϵ\σ}{T}_1^4\mathrm{dA}=2\mathrm{A\ϵA\σ}{T}_1^4=45.4\mathrm{\π}{R}^2{\mathrm{\α}}_2\×{10}^{-8}{T}_1^4---\left(17\right)$

$Q_6\left(t\right)=\underset{A}{\∫}\frac{{\mathrm{\α}}_2\mathrm{\ϵ\σ}{T}_1^4}{1-r}\mathrm{dA}=\frac{A{\mathrm{\α}}_2\mathrm{\ϵ\σ}{T}_1^4}{1-r}=\frac{22.7\mathrm{\π}{R}^2{\mathrm{\α}}_2\mathrm{\ϵ}\×{10}^{-8}{T}_1^4}{1-r}---\left(19\right)$

$Q_7\left(t\right)=\underset{A}{\∫}{h}_1(T_1-T_2)\mathrm{dA}=A{h}_1(T_1-T_2)=4\mathrm{\π}{R}^2{h}_1(T_1-T_2)---\left(20\right)$

$Q_8\left(t\right)=\underset{A}{\∫}{h}_2(T_1-T_3)\mathrm{dA}=A{h}_2(T_1-T_3)=4\mathrm{\π}{R}^2{h}_2(T_1-T_3)---\left(21\right)$

Wherein, the infinitesimal described in step 3 refers to the small unit intercepted on stratosphere balloon, and area is infinitely small;

Step 4, according to principle of energy balance, set up respectively stratosphere balloon by day with the energy-balance equation at night;

For daytime, the gross energy of the capsule cloth of stratosphere balloon is

△Q _film(t)=Q ₁(t)+Q ₂(t)+Q ₃(t)+Q ₄(t)-Q ₅(t)+Q ₆(t)-Q ₇(t)-Q ₈(t) (22)

The gross energy of the inside helium of stratosphere balloon is

△Q _gas(t)=Q ₈(t) (23)

When the energy exchange of stratosphere balloon reaches equilibrium state, △ Q _film(t)=0, △ Q _gas(t)=0, substitution formula (22) and formula (23) obtain capsule cloth and inner helium energy-balance equation by day about stratosphere balloon:

$\left\{\begin{array}{c}{Q}_1\left(t\right)+Q_2\left(t\right)+Q_3\left(t\right)+Q_4\left(t\right)-Q_5\left(t\right)+Q_6\left(t\right)-Q_7\left(t\right)-Q_8\left(t\right)=0\\ Q_8\left(t\right)=0\end{array}\right.---\left(24\right)$

For night, there is no direct solar radiation, sun scattered radiation and earth reflected radiation, i.e. Q ₁(t)=0, Q ₂(t)=0, Q ₃(t)=0, therefore, the capsule cloth of stratosphere balloon and inner helium at the energy-balance equation at night are

$\left\{\begin{array}{c}{Q}_4\left(t\right)-Q_5\left(t\right)+Q_6\left(t\right)-Q_7\left(t\right)-Q_8\left(t\right)=0\\ Q_8\left(t\right)=0\end{array}\right.---\left(25\right)$

The energy-balance equation of step 5, each energy exchange item substitution step 4 that step 3 is obtained, the simple process of iteration in the recycling method of value solving try to achieve stratosphere balloon by day with the temperature at night;

Formula (13) to formula (21) is updated to respectively in formula (24) and formula (25),

$\left\{\begin{array}{c}(\frac{22.7\mathrm{\π}{R}^2{\mathrm{\α}}_2\mathrm{\ϵ}\×{10}^{-8}}{1-r}-45.4\mathrm{\π}{R}^2{\mathrm{\α}}_2\×{10}^{-8})T_1^4-4\mathrm{\π}{R}^2{h}_1{T}_1+[366.8\mathrm{\π}{R}^2{\mathrm{\α}}_1{\left(\frac{R_e}{R_e+H}\right)}^2\cos \frac{\mathrm{\π}|12-t|}{12}\\ +2369.5\mathrm{\π}{R}^2{\mathrm{\α}}_1+214.0\mathrm{\π}{R}^2{\mathrm{\α}}_2{\left(\frac{R_e}{R_e+H}\right)}^2+4\mathrm{\π}{R}^2{h}_1{T}_2]=0\\ T_1-T_3=0\end{array}\right.$

(26)

$\left\{\begin{array}{c}(\frac{22.7\mathrm{\π}{R}^2{\mathrm{\α}}_2\mathrm{\ϵ}\×{10}^{-8}}{1-r}-45.4\mathrm{\π}{R}^2{\mathrm{\α}}_2\×{10}^{-8})T_1^4-4\mathrm{\π}{R}^2{h}_1{T}_1+[214.0\mathrm{\π}{R}^2{\mathrm{\α}}_2{\left(\frac{R_e}{R_e+H}\right)}^2+4\mathrm{\π}{R}^2{h}_1{T}_2]=0\\ T_1-T_3=0\end{array}\right.$

(27)

From (26) and formula (27), when the energy exchange of stratosphere balloon reaches equilibrium state, the capsule Bu Wendu of the stratosphere balloon of day and night equates with inner helium temperature; By the simple process of iteration in method of value solving, equation (26) and (27) are solved respectively, obtain stratosphere balloon by day with capsule Bu Wendu and the inner helium temperature at night.

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